Note: There are several inconsistencies and typos in this question as presented.
- The starting material is given as C\(_4\)H\(_{10}\) (butane), which is an alkane and does not undergo hydroboration-oxidation. It should be an alkene, C\(_4\)H\(_8\) (butene).
- In option (A), the structure for Q (acetone) does not result from the oxidation of P (butan-2-ol). Oxidation of butan-2-ol gives butan-2-one.
We will solve the question by assuming the most plausible intended reaction sequence that aligns with the given options. The sequence from P to R is most coherent if we assume a typo in Q.
Step 1: Determining compound P
Let's assume the starting material is an isomer of butene (C\(_4\)H\(_8\)). The reaction is hydroboration-oxidation, which results in the anti-Markovnikov addition of water across the double bond.
If we start with but-2-ene (CH\(_3\)-CH=CH-CH\(_3\)), hydroboration-oxidation gives butan-2-ol.
P = CH\(_3\)-CH(OH)-CH\(_2\)-CH\(_3\) (Butan-2-ol). This matches the structure of P in option (A).
Step 2: Determining compound Q
Compound P (butan-2-ol, a secondary alcohol) is oxidized with CrO\(_3\) in an anhydrous medium. This reagent oxidizes secondary alcohols to ketones.
\[ \text{CH}_3\text{-CH(OH)-CH}_2\text{-CH}_3 \xrightarrow{\text{CrO}_3} \text{CH}_3\text{-C(=O)-CH}_2\text{-CH}_3 \]
So, Q should be butan-2-one.
Option (A) lists Q as acetone (CH\(_3\)-C(=O)-CH\(_3\)), which is incorrect. This is a likely typo in the question's option. For the sake of finding the "best" answer, let's proceed assuming Q was intended to be butan-2-one.
Step 3: Determining compound R
Compound Q reacts with a Grignard reagent (CH\(_3\)MgBr) followed by acidic hydrolysis (H\(_3\)O\(^+\)). This reaction adds a methyl group to the carbonyl carbon and forms a tertiary alcohol.
Assuming Q is butan-2-one:
\[ \text{CH}_3\text{-C(=O)-CH}_2\text{-CH}_3 + \text{CH}_3\text{MgBr} \rightarrow \text{CH}_3\text{-C(OMgBr)(CH}_3\text{)-CH}_2\text{-CH}_3 \]
Followed by hydrolysis:
\[ \text{CH}_3\text{-C(OMgBr)(CH}_3\text{)-CH}_2\text{-CH}_3 \xrightarrow{\text{H}_3\text{O}^+} \text{CH}_3\text{-C(OH)(CH}_3\text{)-CH}_2\text{-CH}_3 \]
So, R is 2-methylbutan-2-ol. This structure matches R given in option (A).
Step 4: Final Answer:
Based on the analysis, the reaction sequence that produces P (butan-2-ol) and R (2-methylbutan-2-ol) is consistent if the starting material is but-2-ene and Q is butan-2-one. Option (A) correctly identifies P and R, despite having an error in the structure of Q. It is the most plausible answer among the choices.